SEE 2081_RE1031_BP

1. In the survey conducted on 120 households of a village, 70 households are doing homestay business, 50 households are doing agriculture business and 30 households do other work. The sets of household doing homestay and agriculture business are denoted by H and A respectively.
   1. Write the cardinality notation of the number of households who do not do any of the homestay and agriculture business.
   2. Present the above information in a Venn diagram.
   3. Find the number of households doing only one business.
   4. If 10 households who do other work start homestay business, find the ratio of homestay and agriculture business households.
2. Ramesh borrowed a loan of Rs. 2,00,000 from the bank at an annual compound interest rate of 7% per annum. After some time, he repaid Rs. 2,28,980 including the principal and interest to the bank.
   1. How much interest has Ramesh paid?
   2. For how many years has Ramesh used the loan?
   3. If the interest rate is reduced by 1%, how much amount would be paid by Ramesh?
3. The present population of village A is 4500 and village B is 5000. The annual population growth rate of village A is 2%.
   1. What does P denote in the population after T years \(P_T = P\left(1 + \frac{R}{100}\right)^T\)?
   2. If 200 people are added by migration in village A after 1 year, what will be the population after 1 year?
   3. If the population of village B decreases by the same growth rate of village A, what will be the population of village B after 2 years?
4. When Rita came to Nepal from America, she brought 2500 American dollars. The exchange rate was as follows:

   Buying rate of $1	Selling rate of $1
   Rs.127.35	Rs.127.95

   1. Which exchange rate is used to exchange Nepali currency by Rita?
   2. What is the profit or loss for Rita if she exchanges the dollars into Nepali currency and then exchanges back into dollars after two days?Find it.
   3. On the same day, if $1 = Rs.127.35 and Rs.160 = INR Rs.100, how many dollars can be exchanged with Indian Rs.1,20,000?
5. The diagram represents a square based pyramid. Each side of the base is 6 meters and the vertical height is 4 meters.

   1. Write the formula for finding the area of all triangular surfaces of the pyramid.
   2. Find the volume of the pyramid.
   3. Find the total surface area of the pyramid.
6. Given solid object is made up of a cone and a hemisphere. The total height of the object is 17 cm and the diameter of the base is 10 cm.

   1. Write the relation between height and radius of the hemisphere.
   2. Find the total surface area of the solid object.
   3. Will Rs.150 be sufficient to color the surface at the rate of 40 paisa per square cm?
7. A rectangular room has length 12 ft, breadth 8 ft and height 9 ft. There are two windows of size 2.5 ft × 3 ft and two doors of size 6 ft × 2 ft.
   1. Find the total area of four walls, floor and ceiling.
   2. How much less or more is the cost of coloring the four walls excluding the doors and windows at the rate of Rs.175 per square feet than Rs.50,000? Find it.
8. A shop sells shoes and slippers (in pairs) during winter season according to the following table.

   Day	1st Day	2nd Day	3rd Day	4th Day	5th Day
   No. of Shoes	2	4	8	16	..........
   No. of Slippers	3	6	9	12	..........

   1. Write the relationship between arithmetic mean and geometric mean.
   2. How many slippers are sold up to 8th days? Find it.
   3. Compare the total number of shoes and slippers sold up to 8th days.
9. The area and perimeter of a rectangular field are 150 sq. m and 50 m respectively.
   1. Find the length and breadth of the field by forming a quadratic equation.
   2. How much equal part should be subtracted from the length and breadth to get the area 84 sq. m?
10. 1. Write \( \frac{1}{x - 6} \) in positive index of x.
    2. Simplify: \( \frac{a^2}{a - 2b} + \frac{4b^2}{2b - a} \)
    3. Solve: \( 4^{x-2} = 0.25 \)
11. In the given figure, AE // BD, ED // AC and BE // CD.

    1. Write the relationship between the area of parallelogram and triangle standing on the same base and between the same parallel lines.
    2. Prove that ΔABE = ΔBCD.
    3. Compare the area of triangle ABE and trapezium ACDE.
12. In the given figure, PQRS is a cyclic quadrilateral. The side PQ is produced to point T.

    1. Write the relation between ∠PSQ and ∠PRQ.
    2. Verify experimentally that ∠SPR and ∠SQR are equal. (Two circles with radii at least 3 cm are necessary.)
    3. Prove that ∠RQT = ∠PSR.
13. In quadrilateral PQRS, PQ = 5 cm, QR = 4.5 cm, RS = SP = 6 cm and QS = 6.5 cm.
    1. Construct quadrilateral PQRS and then construct a triangle equal to the quadrilateral in area.
    2. Why are the areas of the quadrilateral and triangle equal? Give reason.
14. In the given figure, the height of tower CD is 15√3 m and the height of house AB is 10√3 m. The angle from the roof of the house to the top of the tower is 30°.

    1. What type of angle is formed when the top of the tower is observed from the roof of the house?
    2. Find the height of part DE of the tower.
    3. Calculate the distance between the house and the tower.
    4. Find the angle of depression of the top of the house from the basement.
15. The marks obtained by 50 students of a class in an exam of mathematics with full mark 60 are given below:

    Marks	10–20	20–30	30–40	40–50	50–60
    Number of Students	7	13	15	10	5

    1. Write the class of mode.
    2. Find the value of first quartile (Q₁).
    3. Calculate the average mark.
    4. Find the average mark of students who obtained 40 or more marks.
16. In a box, 5 red and 3 white balls of same size and shape are kept. Two balls are drawn one after another without replacement.
    1. Write the addition law of probability of mutually exclusive events.
    2. Two balls are drawn one after another without replacement from the box. Show the probability of all the possible outcomes in a tree diagram.
    3. Find the probability of getting both white balls from the tree diagram.
    4. Find the difference between the probability of both balls being white if two balls are drawn one after another with replacement and without replacement.